Determine the following:
(a) $\sigma (15)$
(b) $\sigma (77)$
(c) $\sigma (171)$
(d) $\sigma (200)$
The sigma function of a natural number $n$ is the sum of its positive divisors, including 1 and $n$ itself.
(a) $\sigma (15) = 1 + 3 + 5 + 15 = 24$
(b) $\sigma (77) = 1 + 7 + 11 + 77 = 96$
(c) $\sigma (171) = 1 + 3 + 3^2 + 19 + (3\times19) + 171 = 260$
(d) $\sigma(200) = 1 + 2 + 2^2 + 2^3 + 5 + 5^2 + (2 \times 5) + (2^2 \times 5) + (2^3 \times 5) + (2 \times 5^2) + (2^2 \times 5^2) + 200 = 465 $